I have a ragdoll Siamese mix with long fur, and I have found that a simple butt bath, that is, only washing the cats bottom with soap and water on a wash cloth then rinsing the cloth and using it to rinse the soap off while holding her close and speaking softly while you do, then cuddling him or her in a bath towel is very successful in cleaning a mess like this.
First, the closeness and comforting tone of voice help calm kitty and give assurance that all will be OK, and help to build a trusting bond with kitty.
I would also suggest using a comb to separate scissors and skin, and trim up the pantaloons or fur in that area. Additionally, try feeding kitty hairball remedy nightly to help with any hairball related issues.
Remember, since kitty is new that bonding needs to take place in all aspects of care including grooming. Even if kitty gets upset at getting a little wet, he or she will eventually get over it and come to except that sometimes they need to be washed. It would be more stressful to leave that in the kitty's fur since they may not be able to get it all cleaned out themselves, thus resulting in the scooting butt boogie and skid marks on both carpeted and non-carpeted floors and a bigger mess for you to worry about.
The first weeks in home for a kitty should be about bonding and trust. It is not a good idea to just yank the poop out, as like with humans, that area is very sensitive. You can give your pet a treat when you are done to show kitty how much you love him or her and appreciate being allowed to help him or her clean up. This also encourages kitty to come to you when she needs help with grooming issues as well as other issues instead of hiding. I would suggest using one of your old brushes with your scent on it to brush kitty's fur from the beginning and alternate brushing with gentle strokes of the hand so that kitty associates grooming with love and with you.
Praise and treats reinforce kitty's cooperation and good behavior during grooming.
I would avoid trying electric clippers or razors, as they tend to be quite scary and probably irritating to kitty's ears and may cause undue stress and injury for both you and kitty.
Pets are a lot like children in many ways. It is true they are very independent, but nonetheless they still depend on you for the food and water they get, a warm bed, a place to go poop, whether it's walking puppy or keeping kitty's litter clean, and definitely lots of love. The more love you give them, the closer they will get to you and the more they will show you love in return. They show affection, by the way, by bunting (grooming you and rubbing their head against you), snuggling you, rubbing against you when asking for food, and of course bringing you gifts, such as one of their recent kills if they hunt, or even by helping to keep your home bug free. These are just a few ways kitties show their love for you and thank you for all the love and care you give them.